Question

Solve for '$x$' and '$y$', using the method of substitution:
$4x+3y=12$; $x-3y=9$.

• A. ($\frac{1}{5},\frac{4}{5}$)
• B. ($-\frac{21}{5},\frac{2}{5}$)
• C. ($\frac{11}{5},\frac{9}{5}$)
• D. ($\frac{21}{5},-\frac{8}{5}$)

Answer 1

The correct option is D

($\frac{21}{5},-\frac{8}{5}$)

Given that,
$4x+3y=12$ ___(i)
$x-3y=9$ _____(ii)

From equation (ii),
$x=3y+9$ _____(iii)

Pluging this value in equation (i)
$\Rightarrow 4(3y+9)+3y=12$
$\Rightarrow 12y+36+3y=12$
$\Rightarrow 15y=-24$
$\Rightarrow y=-\frac{8}{5}$

Pluging the value of y in equation (iii):
$\Rightarrow x=3y+9$
$\Rightarrow x=-\frac{24}{5}+9$
$\Rightarrow x=-\frac{24}{5}+9$
$\Rightarrow x=\frac{21}{5}$

The solution is ($\frac{21}{5},-\frac{8}{5}$).